University thesis:
Dissertation, Albert-Ludwigs-Universität Freiburg, 2016
Footnote:
cc_by_sa http://creativecommons.org/licenses/by-sa/4.0/deed.de cc
Description:
Abstract: In this thesis, we study a refined Borel regulator from algebraic K-theory of complex numbers to topological K-theory with coefficients in C/Z, which is constructed by Karoubi, Jones and Westbury. <br><br>We investigate the homotopy properties of this regulator and its relation with the xi-invariant of flat vector bundles. We prove that their construction is equivalent to the one given by Atiyah, Patodi and Singer, and explain how this regulator generalizes the Adams e-invariant. The possible homotopy-theoretic constructions of this regulator are also discussed. In particular, we show that there is a unique infinite loop space map from algebraic K-theory of complex numbers to topological K-theory with coefficients in C/Z whose induced homomorphism between homotopy groups is the same as this regulator. The result implies an index theorem analogous to the Bismut-Lott index theorem